theory of charged lepton flavour violation · 2019. 10. 9. · theory of charged lepton flavour...
TRANSCRIPT
Theory of Charged Lepton Flavour Violation
Emilie Passemar* Indiana University/Jefferson Laboratory
10th Anniversary
JPARC Symposium 2019 « Unlocking the Mysteries of Life, Matter and the Universe »
Tsukuba, Japan, September 23 - 26, 2019
*Supported by NSF
Outline
1. Introduction and Motivation
2. Charged Lepton-Flavour Violation: Model discriminating power of muons and tau channels
3. Ex: Non-Standard LFV couplings of the Higgs boson
4. Conclusion and Outlook
1. Introduction and Motivation
1.1 Why study charged leptons?
• In the quest of New Physics, can be sensitive to very high scale:
– Kaon physics: – Charged Leptons:
• At low energy: lots of experiments e.g., MEG, COMET, Mu2e, E-969, BaBar, BelleI-II, BESIII, LHCb huge improvements on measurements and bounds obtained and more expected
• In many cases no SM background: e.g., LFV, EDMs
• For some modes accurate calculations of hadronic uncertainties essential
The new physics flavor scale
K physics: ϵK
sdsd
Λ2⇒ Λ ! 105 TeV
Charged leptons: µ → eγ, µ → e, etc.
µeff
Λ2⇒ Λ ! 103 TeV
There is no exact symmetry that can forbid suchoperatorsAll other bounds on NP, like proton decay, maybe dueto exact symmetry
Y. Grossman Charged lepton theory Lecce, May 6, 2013 p. 10
The new physics flavor scale
K physics: ϵK
sdsd
Λ2⇒ Λ ! 105 TeV
Charged leptons: µ → eγ, µ → e, etc.
µeff
Λ2⇒ Λ ! 103 TeV
There is no exact symmetry that can forbid suchoperatorsAll other bounds on NP, like proton decay, maybe dueto exact symmetry
Y. Grossman Charged lepton theory Lecce, May 6, 2013 p. 10
[µ → eγ]
[ε�]
E
ΛNP
ΛLE
Charged leptons very important to look for New Physics! 4
4
1.2 The Program The very basic of charged leptons
Muon LFC
µ → µγ
(g − 2)µ, (EDM)µ
νe ↔ νµ
νµ ↔ ντ
νe ↔ ντ
NeutrinoOscillations
τ → ℓγ
τ → ℓℓ+i ℓ−
j
Tau LFV
Tau LFC
τ → τγ
(g − 2)τ , (EDM)τ
Muon LFV
µ+ → e+γ
µ+e− → µ−e+µ−N → e+N ′
µ−N → e−Nµ+ → e+e+e−
LFV
Thanks to BabuY. Grossman Charged lepton theory Lecce, May 6, 2013 p. 15
Adapted from Talk by Y. Grossman@CLFV2013
τ → ℓ + hadrons
Emilie Passemar 5
2. Charged Lepton-Flavour Violation
2.1 Introduction and Motivation
• Neutrino oscillations are the first evidence for lepton flavour violation
• How about in the charged lepton sector?
• In the SM with massive neutrinos effective CLFV vertices are tiny due to GIM suppression unobservably small rates!
E.g.:
Emilie Passemar 7
µ → eγ
Br µ → eγ( ) = 3α
32πU µi
*
i=2,3∑ Uei
Δm1i2
MW2
2
< 10−54
ℓ L
Br τ → µγ( ) < 10−40⎡⎣ ⎤⎦
Petcov’77, Marciano & Sanda’77, Lee & Shrock’77…
2.1 Introduction and Motivation
• Neutrino oscillations are the first evidence for lepton flavour violation
• How about in the charged lepton sector?
• In the SM with massive neutrinos effective CLFV vertices are tiny due to GIM suppression unobservably small rates!
E.g.: • Extremely clean probe of beyond SM physics Emilie Passemar 8
µ → eγ
Br µ → eγ( ) = 3α
32πU µi
*
i=2,3∑ Uei
Δm1i2
MW2
2
< 10−54
Petcov’77, Marciano & Sanda’77, Lee & Shrock’77…
eµ
Br τ → µγ( ) < 10−40⎡⎣ ⎤⎦
2.1 Introduction and Motivation
• In New Physics scenarios CLFV can reach observable levels in several channels
• But the sensitivity of particular modes to CLFV couplings is model dependent
• Comparison in muonic and tauonic channels of branching ratios, conversion rates and spectra is model-diagnostic
Emilie Passemar 9
Lepton Flavor Violation in example BSM models � Neutrino-less tτ decays: optimal hunting ground for non-Standard Model LFV effects
� Topologies are similar to those of tτ hadronic decays
� Current limits (down to ~ 10-8), or limits anticipated at next generation e+e- colliders, directlyconfront many New Physics models
David Hitlin 1st Conference on CFLV - Lecce
3
May 8, 2013
Talk by D. Hitlin @ CLFV2013
2.2 CLFV processes: muon decays
• Several processes:
Emilie Passemar 10-/14 (MEG at PSI)
10-15/16 (PSI)10-16/17 → -18 (Mu2e, COMET)
CLFV processes• Muon processes : µ → eγ , µ → eee, µ A, Z( )→ e A, Z( )
MEG’16
BR µ → eee( ) < 1.0 ×10−12
10−15 −10−16
Sindrum
BRµ−eTi < 4.3 ×10−12
Mu2e/COMET 10−16 −10−17
10
Mu3e
Sindrum II
BR µ → eγ( ) < 4.2 ×10−13
6 ×10−14
2.2 CLFV processes: muon decays
• Several processes:
Emilie Passemar
µ → eγ , µ → eee, µ A, Z( )→ e A, Z( )
BR µ → eγ( ) < 4.2 ×10−13
MEG’16
6 ×10−14
10−15 −10−16
Sindrum
Mu2e/COMET 10−16 −10−17
11
Mu3e
Sindrum II
BR µ → eee( ) < 1.0 ×10−12
BRµ−eTi < 4.3 ×10−12
2.2 CLFV processes: tau decays
• Several processes:
• 48 LFV modes studied at Belle and BaBar
•
Emilie Passemar
τ → ℓγ , τ → ℓα ℓβℓ β , τ → ℓY P , S, V , PP , ...
12
2.2 CLFV processes: tau decays
Emilie Passemar
τ → ℓγ , τ → ℓα ℓβℓ β , τ → ℓY P , S, V , PP , ...
13
dec
ays
τ90
% C
.L. u
pper
lim
its fo
r LFV
10−10
9−10
8−10
7−10
6−10
5−10
γ- eγ- µ0 π- e0 π- µη- eη- µ'η- e'η- µ
S0K- e
S0K- µ
0f- e0f- µ
0ρ- e
0ρ- µ*
K- eK
*- µ
K*
- eK
*- µφ- eφ- µ ω- eω- µ
- e+ e- e- e+ e- µ- µ+ µ- e- µ+ µ- µ- e+ µ- e- µ+ e- µ- π+ π- e- π+ π- µ-
K+ π- e-
K+ π- µ- π+
K- e- π+
K- µ-
K+K- e
-K+
K- µ
S0K
S0K- e
S0K
S0K- µ
- π+ e- π- π+ µ- π-
K+ e- π-
K+ µ- π-
K+ e-K
-K+ µ-
KΛ- π
Λ- πΛ-
KΛ-
K
CLEOBaBarBelleLHCbATLASBelle IILHC-HL
γI 0IP 0IS 0IV III Ihh hΛ
• Several processes:
• Expected sensitivity 10-9 or better at LHCb, Belle II, HL-LHC?
•
HL-LHC&HE-LHC’18 Belle II Physics Book’18
Alexey Petrov (WSU & MCTP) HE/HL LHC, Fermilab, 4-6 April 2018
James Miller, 2006
15
A multitude of models…
Emilie Passemar
• Build all D>5 LFV operators:
Ø Dipole:
•
2.3 Effective Field Theory approach
Emilie Passemar
L = LSM + C (5)
ΛO (5) +
Ci(6)
Λ 2 Oi(6)
i∑ + ...
15
See e.g. Black, Han, He, Sher’02 Brignole & Rossi’04 Dassinger, Feldmann, Mannel, Turczyk’07 Matsuzaki & Sanda’08 Giffels et al.’08 Crivellin, Najjari, Rosiek’13 Petrov & Zhuridov’14 Cirigliano, Celis, E.P.’14
Leff
D ⊃ −CD
Λ 2 mτ µσµν PL,RτFµν• Dipole
Dominant in SUSY-GUT and SUSY see-saw scenarios
Rich structure at dim=6
τ !τ
µ !µe.g.
• Build all D>5 LFV operators:
Ø Dipole:
Ø Lepton-quark (Scalar, Pseudo-scalar, Vector, Axial-vector):
•
2.3 Effective Field Theory approach
Emilie Passemar
L = LSM + C (5)
ΛO (5) +
Ci(6)
Λ 2 Oi(6)
i∑ + ...
See e.g. Black, Han, He, Sher’02 Brignole & Rossi’04 Dassinger, Feldmann, Mannel, Turczyk’07 Matsuzaki & Sanda’08 Giffels et al.’08 Crivellin, Najjari, Rosiek’13 Petrov & Zhuridov’14 Cirigliano, Celis, E.P.’14
Leff
D ⊃ −CD
Λ 2 mτ µσµν PL,RτFµν
Leff
S ,V ⊃ −CS ,V
Λ 2 mτ mqGFµ ΓPL,Rτ qΓq
• Dipole
Dominant in SUSY-GUT and SUSY see-saw scenarios
Rich structure at dim=6
Dominant in RPV SUSY and RPC SUSY for large tan(β) and low mA,
leptoquarks
q
q• Scalar (Pseudo-scalar)
τ
µ
ϕ ≡ h0 , H 0 , A0
e.g. Γ ≡ 1
• Dipole
Dominant in SUSY-GUT and SUSY see-saw scenarios
Rich structure at dim=6
Dominant in RPV SUSY and RPC SUSY for large tan(β) and low mA ,
leptoquarks
q
q• Scalar (Pseudo-scalar)
• VectorEnhanced in Type III seesaw (Z-penguin),
Type II seesaw, LRSM, leptoquarks
(Axial-vector) qq
μ eτ µ
Γ ≡ γ µ
• Build all D>5 LFV operators:
Ø Dipole:
Ø Lepton-quark (Scalar, Pseudo-scalar, Vector,
Axial-vector):
Ø Integrating out heavy quarks generates gluonic operator
•
2.3 Effective Field Theory approach
Emilie Passemar
L = LSM + C (5)
ΛO (5) +
Ci(6)
Λ 2 Oi(6)
i∑ + ...
17
See e.g. Black, Han, He, Sher’02 Brignole & Rossi’04 Dassinger, Feldmann, Mannel, Turczyk’07 Matsuzaki & Sanda’08 Giffels et al.’08 Crivellin, Najjari, Rosiek’13 Petrov & Zhuridov’14 Cirigliano, Celis, E.P.’14
Leff
D ⊃ −CD
Λ 2 mτ µσµν PL,RτFµν
Leff
S ⊃ −CS ,V
Λ 2 mτ mqGFµ ΓPL,Rτ qΓq
1Λ 2 µPL,RτQQ à
Leff
G ⊃ −CG
Λ 2 mτGFµPL,Rτ Gµνa Ga
µν
• Dipole
Dominant in SUSY-GUT and SUSY see-saw scenarios
Rich structure at dim=6
Dominant in RPV SUSY and RPC SUSY for large tan(β) and low mA,
leptoquarks
q
q• Scalar (Pseudo-scalar)
τ
µ
ϕ ≡ h0 , H 0 , A0
Importance of this operator emphasized in Petrov & Zhuridov’14
• Build all D>5 LFV operators:
Ø Dipole:
Ø Lepton-quark (Scalar, Pseudo-scalar, Vector,
Axial-vector):
Ø 4 leptons (Scalar, Pseudo-scalar, Vector, Axial-vector):
•
2.3 Effective Field Theory approach
Emilie Passemar
L = LSM + C (5)
ΛO (5) +
Ci(6)
Λ 2 Oi(6)
i∑ + ...
18
See e.g. Black, Han, He, Sher’02 Brignole & Rossi’04 Dassinger, Feldmann, Mannel, Turczyk’07 Matsuzaki & Sanda’08 Giffels et al.’08 Crivellin, Najjari, Rosiek’13 Petrov & Zhuridov’14 Cirigliano, Celis, E.P.’14
LeffD ⊃ −
CD
Λ 2 mτ µσµν PL,RτFµν
Leff
S ⊃ −CS ,V
Λ 2 mτ mqGFµ ΓPL,Rτ qΓq
Leff
4ℓ ⊃ −CS ,V
4ℓ
Λ 2 µ ΓPL,Rτ µ ΓPL,Rµ
Γ ≡ 1 ,γ µ
• Dipole
Dominant in SUSY-GUT and SUSY see-saw scenarios
Rich structure at dim=6
Dominant in RPV SUSY and RPC SUSY for large tan(β) and low mA ,
leptoquarks
q
q• Scalar (Pseudo-scalar)
• 4 Leptons, ...
Type II and III seesaw, RPV SUSY, LRSM
• VectorEnhanced in Type III seesaw (Z-penguin),
Type II seesaw, LRSM, leptoquarks
(Axial-vector) qq
μ e
τµ
µ
µ
e.g.
• Build all D>5 LFV operators:
Ø Dipole:
Ø Lepton-quark (Scalar, Pseudo-scalar, Vector,
Axial-vector):
Ø Lepton-gluon (Scalar, Pseudo-scalar):
Ø 4 leptons (Scalar, Pseudo-scalar, Vector, Axial-vector):
• Each UV model generates a specific pattern of them
•
2.3 Effective Field Theory approach
Emilie Passemar
L = LSM + C (5)
ΛO (5) +
Ci(6)
Λ 2 Oi(6)
i∑ + ...
19
See e.g. Black, Han, He, Sher’02 Brignole & Rossi’04 Dassinger, Feldmann, Mannel, Turczyk’07 Matsuzaki & Sanda’08 Giffels et al.’08 Crivellin, Najjari, Rosiek’13 Petrov & Zhuridov’14 Cirigliano, Celis, E.P.’14
Leff
D ⊃ −CD
Λ 2 mτ µσµν PL,RτFµν
Leff
S ⊃ −CS ,V
Λ 2 mτ mqGFµ ΓPL,Rτ qΓq
Leff
G ⊃ −CG
Λ 2 mτGFµPL,Rτ Gµνa Ga
µν
Leff
4ℓ ⊃ −CS ,V
4ℓ
Λ 2 µ ΓPL,Rτ µ ΓPL,Rµ
Γ ≡ 1 ,γ µ
2.4 Model discriminating power of muon processes
Emilie Passemar
• Summary table:
• The notion of “best probe” (process with largest decay rate) is model dependent
• If observed, compare rate of processes key handle on relative strength between operators and hence on the underlying mechanism
Discriminating power: μLFV matrixCirigliano@Beauty2014
20
2.4 Model discriminating power of muon processes
• Summary table:
• µ → eγ vs. µ → 3e relative strength between dipole and 4L operators
Discriminating power: μLFV matrix
• μ → 3e vs μ →eγ: relative strength of dipole and 4L operators
6 ×10-3
Discriminating power: μLFV matrix
Emilie Passemar
Cirigliano@Beauty2014
21
2.4 Model discriminating power of muon processes
• Summary table:
• µ →eγ vs. µ → e conversion relative strength between dipole and quark operators
Discriminating power: μLFV matrix
• μ →e vs μ →eγ and target-dependence of μ →e conversion: relative strength of dipole and quark operators
Discriminating power: μLFV matrixCirigliano@Beauty2014
22 Emilie Passemar
BR for �� e conversion
• For µ →e conversion, target dependence of the amplitude is different for V,D or S models Cirigliano, Kitano, Okada, Tuzon’09
μ→e vs μ→eγ • Assume dipole dominance:
Kitano-Koike-Okada ‘02VC-Kitano-Okada-Tuzon ‘09
€
B(µ → e,Z)B(µ → eγ)
O(α/π)
Z
Pattern controlled by: 1) Behavior of overlap integrals 2) Total capture rate (sensitive to nuclear structure) Deviations would indicate presence of scalar / vector terms
23 Emilie Passemar
2.5 Model discriminating power of Tau processes
Emilie Passemar
• Summary table:
• In addition to leptonic and radiative decays, hadronic decays are very important sensitive to large number of operators!
• But need reliable determinations of the hadronic part: form factors and decay constants(e.g. fη, fη�)
Discriminating power: τLFV matrix
24
Celis,Cirigliano,E.P.’14
2.5 Model discriminating power of Tau processes
• Summary table:
• Form factors for τ → µ(�)ππdetermined using dispersive techniques • Hadronic part:
• 2-channel unitarity condition is solved with I=0S-waveππandKKsca2eringdataasinput
Discriminating power: τLFV matrix
25
Celis,Cirigliano,E.P.’14
Celis,Cirigliano,E.P.’14Daubetal’13
Donoghue,Gasser,Leutwyler’90 Moussallam’99
Form factors• Two channel unitarity condition (ππ, KK) (OK up to √s ~ 1.4 GeV)
n = ππ, KK
• General solution:
Canonical solution falling as 1/s for large s (obey un-subtracted dispersion relation)
Polynomials determined by
matching to ChPT
• Solved iteratively, using input on s-wave I=0 meson meson scattering
n = ππ , KK
Hµ = ππ Vµ − Aµ( )eiLQCD 0 = Lorentz struct.( )µ
iFi s( )
s = p
π + + pπ −( )2
with
Emilie Passemar
2.5 Model discriminating power of Tau processes
• Two handles:
Ø Branching ratios: with FM dominant LFV mode for model M
Ø Spectra for > 2 bodies in the final state:
and
RF ,M ≡
Γ τ → F( )Γ τ → FM( )
dR
π +π − ≡1
Γ τ → µγ( )dΓ τ → µπ +π −( )
d s
dBR τ → µπ +π −( )d s
26 Emilie Passemar
Celis, Cirigliano, E.P.’14
2.6 Model discriminating of BRs • Studies in specific models
Disentangle the underlying dynamics of NP
Buras et al.’10
to the ranges given in Table 3 for the SM4 and the LHT model.
4.7 Patterns of Correlations and Comparison with the MSSM
and the LHT
In [4,55] a number of correlations have been identified that allow to distinguish the LHT
model from the MSSM. These results are recalled in Table 3. In the last column of this
table we also show the results obtained in the SM4. We observe:
• For most of the ratios considered here the values found in the SM4 are significantly
larger than in the LHT and by one to two orders of magnitude larger than in the
MSSM.
• In the case of µ ! e conversion the predictions of the SM4 and the LHT model
are very uncertain but finding said ratio to be of order one would favour the SM4
and the LHT model over the MSSM.
• Similarly, in the case of several ratios considered in this table, finding them to be
of order one will choose the SM4 as a clear winner in this competition.
ratio LHT MSSM (dipole) MSSM (Higgs) SM4
Br(µ�!e�e+e�)
Br(µ!e�) 0.02. . . 1 ⇠ 6 · 10�3 ⇠ 6 · 10�3 0.06 . . . 2.2
Br(⌧�!e�e+e�)
Br(⌧!e�) 0.04. . . 0.4 ⇠ 1 · 10�2 ⇠ 1 · 10�2 0.07 . . . 2.2
Br(⌧�!µ�µ+µ�)
Br(⌧!µ�) 0.04. . . 0.4 ⇠ 2 · 10�3 0.06 . . . 0.1 0.06 . . . 2.2
Br(⌧�!e�µ+µ�)
Br(⌧!e�) 0.04. . . 0.3 ⇠ 2 · 10�3 0.02 . . . 0.04 0.03 . . . 1.3
Br(⌧�!µ�e+e�)
Br(⌧!µ�) 0.04. . . 0.3 ⇠ 1 · 10�2 ⇠ 1 · 10�2 0.04 . . . 1.4
Br(⌧�!e�e+e�)
Br(⌧�!e�µ+µ�) 0.8. . . 2 ⇠ 5 0.3. . . 0.5 1.5 . . . 2.3
Br(⌧�!µ�µ+µ�)
Br(⌧�!µ�e+e�) 0.7. . . 1.6 ⇠ 0.2 5. . . 10 1.4 . . . 1.7
R(µTi!eTi)Br(µ!e�) 10�3
. . . 102 ⇠ 5 · 10�3 0.08 . . . 0.15 10�12. . . 26
Table 3: Comparison of various ratios of branching ratios in the LHT model [55], the
MSSM without [63, 64] and with significant Higgs contributions [65, 66] and the SM4
calculated here.
20
2.7 Discriminating power of τ → µ(�)ππ decays
• Two basic handles: 2) Spectra in > 2 body decays
Spin and isospin of the hadronic operator leave imprint in the spectrum
Celis-VC-Passemar 1403.5781
Leff
D ⊃ −CD
Λ 2 mτ µσµν PL,RτFµν
28 Emilie Passemar
• DipoleDominant in SUSY-GUT and
SUSY see-saw scenarios
Rich structure at dim=6
τ !τ
µ !µ
Celis, Cirigliano, E.P.’14
2.7 Discriminating power of τ → µ(�)ππ decays
• Two basic handles: 2) Spectra in > 2 body decays
Spin and isospin of the hadronic operator leave imprint in the spectrum
Celis-VC-Passemar 1403.5781
• Two basic handles: 2) Spectra in > 2 body decays
Spin and isospin of the hadronic operator leave imprint in the spectrum
Celis-VC-Passemar 1403.5781
Leff
D ⊃ −CD
Λ 2 mτ µσµν PL,RτFµν
Leff
S ⊃ −CS
Λ 2 mτ mqGFµPL,Rτ qq
29 Emilie Passemar
• Two basic handles: 2) Spectra in > 2 body decays
Spin and isospin of the hadronic operator leave imprint in the spectrum
Celis-VC-Passemar 1403.5781
• Two basic handles: 2) Spectra in > 2 body decays
Spin and isospin of the hadronic operator leave imprint in the spectrum
Celis-VC-Passemar 1403.5781
• Two basic handles: 2) Spectra in > 2 body decays
Spin and isospin of the hadronic operator leave imprint in the spectrum
Celis-VC-Passemar 1403.5781
Different distributions according to the operator!
Leff
D ⊃ −CD
Λ 2 mτ µσµν PL,RτFµν
Leff
S ⊃ −CS
Λ 2 mτ mqGFµPL,Rτ qq
Leff
G ⊃ −CG
Λ 2 mτGFµPL,Rτ Gµνa Ga
µν
30
2.7 Discriminating power of τ → µ(�)ππ decays
3. Ex: Charged Lepton-Flavour Violation and Higgs Physics
3.1 Non standard LFV Higgs coupling
•
• Arise in several models Cheng, Sher’97, Goudelis, Lebedev,Park’11
Davidson, Grenier’10
• Order of magnitude expected No tuning: • In concrete models, in general further parametrically suppressed
IntheSM: vSMh i
ij ijmY δ=
ΔLY = −
λij
Λ 2 fLi fR
j H( )H †H −Yij fLi fR
j( )hGoudelis, Lebedev, Park’11 Davidson, Grenier’10 Harnik, Kopp, Zupan’12 Blankenburg, Ellis, Isidori’12 McKeen, Pospelov, Ritz’12 Arhrib, Cheng, Kong’12
32 Emilie Passemar
LY = −mi fL
i fRi − h YeµeLµR +YeτeLτ R +Yµτ µLτ R( ) + ...
Cheng, Sher’97
Emilie Passemar 11
1.1 Introduction:
• Consider the possibility of non-standard LFV couplings of the Higgs
• LFV has been discovered in the neutrino sector: neutrino oscillations why not for the charged leptons?
• Arise in several models
• Order of magnitude expected: No tuning: In concrete models, in general further parametrically suppressed
1.1 Introduction
Cheng, Sher’97, Goudelis, Lebedev,Park’11 Davidson, Grenier’10
Emilie Passemar 8
Yτµ"
Jefferson Lab, Mar 2 2015J. Zupan Rare Higgs Decays
• what is a reasonable aim for precision on Yij?
• if off-diagonals are large ⇒ spectrum in general not hierarchical
• no tuning, if
• in concrete models it will be typically further suppressed parametrically
a general benchmark
15
Cheng, Sher, 1987
see e.g, Dery, Efrati, Nir, Soreq, Susic, 1408.1371;Dery, Efrati, Hochberg, Nir, 1302.3229;
Arhrib, Cheng, Kong, 1208.4669
Cheng, Sher’97
e.g.: Arhrib et al’12 Derry et al.’13,’14,
2.1 Introduction
LY = −Yij fLi fR
j( )h + h.c. + ...In the SM:
vSMh i
ij ijmY δ=
LY = −mi fL
i fRi − h YeµeLµR +YeτeLτ R +Yµτ µLτ R( ) + ...
3.1 Non standard LFV Higgs coupling
•
• High energy : LHC
• Low energy : D, S operators
−Yij fLi fR
j( )h
In the SM: vSMh i
ij ijmY δ=
Yτµ
Hadronic part treated with perturbative QCD
ΔLY = −
λij
Λ 2 fLi fR
j H( )H †H −Yij fLi fR
j( )hGoudelis, Lebedev, Park’11 Davidson, Grenier’10 Harnick, Koop, Zupan’12 Blankenburg, Ellis, Isidori’12 McKeen, Pospelov, Ritz’12 Arhrib, Cheng, Kong’12
33 Emilie Passemar
Harnick, Koop, Zupan’12 Blankenburg, Ellis, Isidori’12 McKeen, Pospelov, Ritz’12 Arhrib, Cheng, Kong’12
3.1 Non standard LFV Higgs coupling
•
• High energy : LHC
• Low energy : D, S, G operators
−Yij fLi fR
j( )h
Yτµ
Hadronic part treated with perturbative QCD
ΔLY = −
λij
Λ 2 fLi fR
j H( )H †H −Yij fLi fR
j( )h
Reverse the process
+
Yτµ
Hadronic part treated with non-perturbative QCD
Goudelis, Lebedev, Park’11 Davidson, Grenier’10
In the SM: vSMh i
ij ijmY δ=
34 Emilie Passemar
3.2 Constraints in the τµ sector
• At low energy Ø τ → µππ :
ρ 0f
Dominated by Ø ρ(770) (photon mediated) Ø f0(980) (Higgs mediated)
+hh
35 Emilie Passemar
3.2 Constraints in the τµ sector
Emilie Passemar 36 Belle’08’11’12 except last from CLEO’97
Bound:
Yµτ
h 2+ Yτµ
h 2≤ 0.13
3.2 Constraints in the τµ sector
• Constraints from LE: Ø τ → µγ :best constraints
but loop level sensitive to UV completion of the theory
Ø τ → µππ : tree level diagrams robust handle on LFV
• Constraints from HE: LHC wins for τ µ!
• Opposite situation forµe!
• For LFV Higgs and nothing else: LHC bound
BR τ → µγ( ) < 2.2 ×10−9
BR τ → µππ( ) < 1.5 ×10−11
14 9 Summary
| τµ
|Y-410 -310 -210 -110 1
|
µτ|Y
-410
-310
-210
-110
1 (8 TeV)-119.7 fbCMS
BR<0.1%
BR<1%
BR<10%
BR<50%
ττ→ATLAS H
observed
expectedτµ→H
µ 3→τ
γ µ →τ
2/vτmµ
|=mµτ
Yτµ|Y
Figure 6: Constraints on the flavour-violating Yukawa couplings, |Yµt| and |Ytµ|. The blackdashed lines are contours of B(H ! µt) for reference. The expected limit (red solid line)with one sigma (green) and two sigma (yellow) bands, and observed limit (black solid line)are derived from the limit on B(H ! µt) from the present analysis. The shaded regions arederived constraints from null searches for t ! 3µ (dark green) and t ! µg (lighter green). Theyellow line is the limit from a theoretical reinterpretation of an ATLAS H ! tt search [4]. Thelight blue region indicates the additional parameter space excluded by our result. The purplediagonal line is the theoretical naturalness limit YijYji mimj/v
2.
9 Summary
The first direct search for lepton-flavour-violating decays of a Higgs boson to a µ-t pair, basedon the full 8 TeV data set collected by CMS in 2012 is presented. It improves upon previouslypublished indirect limits [4, 26] by an order of magnitude. A slight excess of events with asignificance of 2.4 s is observed, corresponding to a p-value of 0.010. The best fit branchingfraction is B(H ! µt) = (0.84+0.39
�0.37)%. A constraint of B(H ! µt) < 1.51% at 95% confidencelevel is set. The limit is used to constrain the Yukawa couplings,
p
|Yµt|2 + |Ytµ|
2 < 3.6 ⇥ 10�3.It improves the current bound by an order of magnitude.
Acknowledgments
We congratulate our colleagues in the CERN accelerator departments for the excellent perfor-mance of the LHC and thank the technical and administrative staffs at CERN and at other CMSinstitutes for their contributions to the success of the CMS effort. In addition, we gratefullyacknowledge the computing centres and personnel of the Worldwide LHC Computing Gridfor delivering so effectively the computing infrastructure essential to our analyses. Finally, weacknowledge the enduring support for the construction and operation of the LHC and the CMSdetector provided by the following funding agencies: BMWFW and FWF (Austria); FNRS andFWO (Belgium); CNPq, CAPES, FAPERJ, and FAPESP (Brazil); MES (Bulgaria); CERN; CAS,MoST, and NSFC (China); COLCIENCIAS (Colombia); MSES and CSF (Croatia); RPF (Cyprus);MoER, ERC IUT and ERDF (Estonia); Academy of Finland, MEC, and HIP (Finland); CEA andCNRS/IN2P3 (France); BMBF, DFG, and HGF (Germany); GSRT (Greece); OTKA and NIH(Hungary); DAE and DST (India); IPM (Iran); SFI (Ireland); INFN (Italy); MSIP and NRF (Re-
Plot from Harnik, Kopp, Zupan’12 updated by CMS’15
τ → µππ
3.3 Hint of New Physics in h � τ µ ?
CMS’15
B2TiP, KEK, Tsukuba, Oct 28 2015J. Zupan Higgs and Lepton Flavor Violation
• hint of a signal in h→τ"?
• CMS: Br(h→τ")=(0.89±0.39)%
• ATLAS: Br(H→"τ)=(0.77±0.62)%
11
h→τ" exp. info
CMS-HIG-14-005
ATLAS, 1508.03372 ATLAS’15 BR h →τµ( ) = 0.84−0.37
+0.39( )% BR h →τµ( ) = 0.53 ± 0.51( )%@2.4σ @1σ
38
3.3 Hint of New Physics in h � τ µ ?
39
CMS’17
23
| τµ
|Y5−10 4−10 3−10 2−10 1−10
|
µ τ|Y
5−10
4−10
3−10
2−10
1−10
(13 TeV)-136.0 fbCMS
B<0.01%
B<0.1%
B<1%
B<10%
B<50%
CMS 8TeVobserved
τµ →expected H
µ 3→τ
γ µ →τ
2/vτmµ
|=mµ τ
Yτ µ
|Y
| τe|Y
5−10 4−10 3−10 2−10 1−10
|
eτ|Y
5−10
4−10
3−10
2−10
1−10
(13 TeV)-136.0 fbCMS
B<0.01%
B<0.1%
B<1%
B<10%
B<50%
CMS 8TeVobservedτ e→expected H
3e→τ
γ e →τ
2/vτme
|=m eτ
Yτe
|Y
Figure 10: Constraints on the flavour violating Yukawa couplings, |Yµt|, |Ytµ| (left) and|Yet|, |Yte| (right), from the BDT result. The expected (red dashed line) and observed (blacksolid line) limits are derived from the limit on B(H ! µt) and B(H ! et) from the presentanalysis. The flavour-diagonal Yukawa couplings are approximated by their SM values. Thegreen (yellow) band indicates the range that is expected to contain 68% (95%) of all observedlimit excursions from the expected limit. The shaded regions are derived constraints from nullsearches for t ! 3µ or t ! 3e (dark green) [41, 92, 93] and t ! µg or t ! eg (lightergreen) [41, 93]. The green hashed region is derived by the CMS direct search presented inthis paper. The blue solid lines are the CMS limits from [44] (left) and [45](right). The purplediagonal line is the theoretical naturalness limit |YijYji| mimj/v
2 [41].
AcknowledgmentsWe congratulate our colleagues in the CERN accelerator departments for the excellent perfor-mance of the LHC and thank the technical and administrative staffs at CERN and at otherCMS institutes for their contributions to the success of the CMS effort. In addition, we grate-fully acknowledge the computing centres and personnel of the Worldwide LHC ComputingGrid for delivering so effectively the computing infrastructure essential to our analyses. Fi-nally, we acknowledge the enduring support for the construction and operation of the LHCand the CMS detector provided by the following funding agencies: BMWFW and FWF (Aus-tria); FNRS and FWO (Belgium); CNPq, CAPES, FAPERJ, and FAPESP (Brazil); MES (Bulgaria);CERN; CAS, MoST, and NSFC (China); COLCIENCIAS (Colombia); MSES and CSF (Croatia);RPF (Cyprus); SENESCYT (Ecuador); MoER, ERC IUT, and ERDF (Estonia); Academy of Fin-land, MEC, and HIP (Finland); CEA and CNRS/IN2P3 (France); BMBF, DFG, and HGF (Ger-many); GSRT (Greece); OTKA and NIH (Hungary); DAE and DST (India); IPM (Iran); SFI(Ireland); INFN (Italy); MSIP and NRF (Republic of Korea); LAS (Lithuania); MOE and UM(Malaysia); BUAP, CINVESTAV, CONACYT, LNS, SEP, and UASLP-FAI (Mexico); MBIE (NewZealand); PAEC (Pakistan); MSHE and NSC (Poland); FCT (Portugal); JINR (Dubna); MON,RosAtom, RAS, RFBR and RAEP (Russia); MESTD (Serbia); SEIDI, CPAN, PCTI and FEDER(Spain); Swiss Funding Agencies (Switzerland); MST (Taipei); ThEPCenter, IPST, STAR, andNSTDA (Thailand); TUBITAK and TAEK (Turkey); NASU and SFFR (Ukraine); STFC (UnitedKingdom); DOE and NSF (USA).
Individuals have received support from the Marie-Curie programme and the European Re-search Council and Horizon 2020 Grant, contract No. 675440 (European Union); the LeventisFoundation; the A. P. Sloan Foundation; the Alexander von Humboldt Foundation; the Belgian
τ → µππ
18
), %τµ→(HΒ95% CL limit on 0 2 4 6 8 10 12 14
0.25% (0.25%) τµ→H
1.79% (1.62%) , VBFeτµ
2.27% (1.98%) , 2 Jetseτµ
1.34% (1.19%) , 1 Jeteτµ
1.30% (0.83%) , 0 Jetseτµ
0.51% (0.58%) , VBF
hτµ
0.56% (0.94%) , 2 Jets
hτµ
0.53% (0.56%) , 1 Jet
hτµ
0.51% (0.43%) , 0 Jets
hτµ
: BDT fitτµ→hObservedMedian expected68% expected95% expected
(13 TeV)-135.9 fbCMS
), %τµ→(HΒ95% CL limit on 0 2 4 6 8 10 12 14
0.51% (0.49%) τµ→H
1.40% (1.73%) , VBFeτµ
3.33% (3.23%) , 2 Jetseτµ
1.35% (1.47%) , 1 Jeteτµ
1.08% (1.01%) , 0 Jetseτµ
1.30% (1.41%) , VBF
hτµ
1.65% (2.12%) , 2 Jets
hτµ
1.74% (1.26%) , 1 Jet
hτµ
1.04% (1.14%) , 0 Jets
hτµ
fitcol
: Mτµ→hObservedMedian expected68% expected95% expected
(13 TeV)-135.9 fbCMS
Figure 6: Observed and expected 95% CL upper limits on the B(H ! µt) for each individualcategory and combined. Left: BDT fit analysis. Right: Mcol fit analysis.
Table 6: Expected and observed upper limits at 95% CL and best fit branching fractions inpercent for each individual jet category, and combined, in the H ! et process obtained withthe BDT fit analysis.
Expected limits (%)0-jet 1-jet 2-jets VBF Combined
etµ <0.90 <1.59 <2.54 <1.84 <0.64eth <0.79 <1.13 <1.59 <0.74 <0.49et <0.37
Observed limits (%)0-jet 1-jet 2-jets VBF Combined
etµ <1.22 <1.66 <2.25 <1.10 <0.78eth <0.73 <0.81 <1.94 <1.49 <0.72et <0.61
Best fit branching fractions (%)0-jet 1-jet 2-jets VBF Combined
etµ 0.47 ± 0.42 0.17 ± 0.79 �0.42 ± 1.01 �1.54 ± 0.44 0.18 ± 0.32eth �0.13 ± 0.39 �0.63 ± 0.40 0.54 ± 0.53 0.70 ± 0.38 0.33 ± 0.24et 0.30 ± 0.18
BR h →τµ( ) = 0.25 ± 0.25( )% 13 TeV@CMS CMS’17
8 Results
The best-fit branching ratios and upper limits are computed while assuming B(H ! µ⌧) = 0 for theH ! e⌧ search and B(H ! e⌧) = 0 for the H ! µ⌧ search. The best-fit values of the LFV Higgs bosonbranching ratios are equal to (0.15+0.18
�0.17)% and (�0.22 ± 0.19)% for the H ! e⌧ and H ! µ⌧ search,respectively. In the absence of a significant excess, upper limits on the LFV branching ratios are set fora Higgs boson with mH = 125 GeV. The observed (median expected) 95% CL upper limits are 0.47%(0.34+0.13
�0.10 %) and 0.28% (0.37+0.14�0.10 %) for the H ! e⌧ and H ! µ⌧ searches, respectively. These limits
are significantly lower than the corresponding Run 1 limits of Refs. [7, 8]. The breakdown of contributionsfrom di�erent signal regions is shown in Figure 4.
) in %τ e→ H(Β95% CL upper limit on 0 1 2 3 4 5 6
ATLAS Observed
σ 1±Expected
σ 2±Expected
-1 = 13 TeV, 36.1 fbs
VBFµτe1.59 (exp)1.69 (obs)
-1.24
+1.72 = 0.07µ
µτe0.58 (exp)0.81 (obs)
-0.31
+0.31 = 0.30µ
hadτe0.54 (exp)0.72 (obs)
-0.26
+0.27 = 0.23µ
non-VBFhadτe0.65 (exp)1.00 (obs)
-0.32
+0.33 = 0.42µ
non-VBFµτe0.61 (exp)0.80 (obs)
-0.31
+0.31 = 0.25µ
τe0.34 (exp)0.47 (obs)
-0.17
+0.18 = 0.15µ
VBFhadτe0.97 (exp)0.84 (obs)
-0.58
+0.60 = -0.35µ
) in %τµ → H(Β95% CL upper limit on 0 1 2 3 4 5 6
ATLAS Observed
σ 1±Expected
σ 2±Expected
-1 = 13 TeV, 36.1 fbs
VBFe
τµ
1.64 (exp)1.08 (obs)
-0.89
+0.89 = -1.28µ
eτµ
0.66 (exp)0.44 (obs)
-0.31
+0.31 = -0.38µ
hadτµ
0.44 (exp)0.41 (obs)
-0.23
+0.23 = -0.07µ
non-VBFhad
τµ
0.57 (exp)0.49 (obs)
-0.32
+0.31 = -0.21µ
non-VBFe
τµ
0.72 (exp)0.57 (obs)
-0.35
+0.35 = -0.24µ
τµ
0.37 (exp)0.28 (obs)
-0.19
+0.19 = -0.22µ
VBFhad
τµ
0.96 (exp)0.94 (obs)
-0.58
+0.58 = -0.09µ
Figure 4: Upper limits at 95% CL on the LFV branching ratios of the Higgs boson, H ! e⌧ (left) and H ! µ⌧(right), indicated by solid and dashed lines. Best-fit values of the branching ratios (µ) are also given, in %. The limitsare computed while assuming that either B(H ! µ⌧) = 0 (left) or B(H ! e⌧) = 0 (right). First, the results of thefits are shown, when only the data of an individual channel or of an individual category are used; in these casesthe signal and control regions from all other channels/categories are removed from the fit. These results are finallycompared with the full fit displayed in the last row.
The branching ratio of the LFV Higgs boson decay is related to the non-diagonal Yukawa coupling matrixelements [84] by the formula
|Y ⌧ |2 + |Y⌧` |
2 =8⇡mH
B(H ! `⌧)
1 � B(H ! `⌧)�H (SM),
where �H (SM) = 4.07 MeV [85] stands for the Higgs boson width as predicted by the Standard Model.Thus, the observed limits on the branching ratio correspond to the following limits on the coupling matrixelements:
p|Y⌧e |
2 + |Ye⌧ |2 < 0.0020, and
q|Y⌧µ |
2 + |Yµ⌧ |2 < 0.0015. Figure 5 shows the limits on the
individual coupling matrix elements Y⌧` and Y ⌧ together with the limits from the ATLAS Run 1 analysisand from ⌧ ! `� searches [84, 86].
14
4−10 3−10 2−10 1−10|
τe |Y
4−10
3−10
2−10
1−10|e
τ|Y
γ e → τ <
10
%Β
< 1
%Β
< 0
.1%
Β
< 0
.01
%Β
< 5
0%
Β
| < n.l.
eτ
Yτe
|Y
-1=13 TeV, 36.1 fbs
ATLAS Observed
σ 1±Expected
σ 2±Expected
ATLAS Run 1
4−10 3−10 2−10 1−10|
τ µ|Y
4−10
3−10
2−10
1−10|µ
τ|Y
γ µ → τ
< 1
0%
Β
< 1
%Β
< 0
.1%
Β
< 0
.01
%Β
< 5
0%
Β
| < n.l.
µ τ
Yτ µ
|Y
-1=13 TeV, 36.1 fbs
ATLAS Observed
σ 1±Expected
σ 2±Expected
ATLAS Run 1
Figure 5: Upper limits on the absolute value of the couplings Y⌧` and Y ⌧ together with the limits from the ATLASRun 1 analysis (light grey line) and the most stringent indirect limits from ⌧ ! `� searches (dark purple region).Also indicated are limits corresponding to di�erent branching ratios (0.01%, 0.1%, 1%, 10% and 50%) and thenaturalness limit (denoted n.l.) |Y⌧`Y ⌧ | .
m⌧m`v
[84] where v is the vacuum expectation value of the Higgs field.
9 Conclusions
Direct searches for the decays H ! e⌧ and H ! µ⌧ are performed with proton–proton collisionsrecorded by the ATLAS detector at the LHC corresponding to an integrated luminosity of 36.1 fb�1 at acentre-of-mass energy of
ps = 13 TeV. No significant excess is observed above the expected background
from Standard Model processes. The observed (expected) upper limits at 95% confidence level on thebranching ratios of H ! e⌧ and H ! µ⌧ are 0.47% (0.34+0.13
�0.10 %) and 0.28% (0.37+0.14�0.10 %), respectively.
These limits are more stringent by a factor of 2 (5) than the corresponding limits for the H ! e⌧ (H ! µ⌧)decay determined by ATLAS at
ps = 8 TeV.
Acknowledgements
We thank CERN for the very successful operation of the LHC, as well as the support sta� from ourinstitutions without whom ATLAS could not be operated e�ciently.
We acknowledge the support of ANPCyT, Argentina; YerPhI, Armenia; ARC, Australia; BMWFWand FWF, Austria; ANAS, Azerbaijan; SSTC, Belarus; CNPq and FAPESP, Brazil; NSERC, NRC andCFI, Canada; CERN; CONICYT, Chile; CAS, MOST and NSFC, China; COLCIENCIAS, Colombia;MSMT CR, MPO CR and VSC CR, Czech Republic; DNRF and DNSRC, Denmark; IN2P3-CNRS,CEA-DRF/IRFU, France; SRNSFG, Georgia; BMBF, HGF, and MPG, Germany; GSRT, Greece; RGC,Hong Kong SAR, China; ISF and Benoziyo Center, Israel; INFN, Italy; MEXT and JSPS, Japan; CNRST,Morocco; NWO, Netherlands; RCN, Norway; MNiSW and NCN, Poland; FCT, Portugal; MNE/IFA,Romania; MES of Russia and NRC KI, Russian Federation; JINR; MESTD, Serbia; MSSR, Slovakia;ARRS and MIZä, Slovenia; DST/NRF, South Africa; MINECO, Spain; SRC and Wallenberg Foundation,Sweden; SERI, SNSF and Cantons of Bern and Geneva, Switzerland; MOST, Taiwan; TAEK, Turkey;
15
3.3 Hint of New Physics in h � τ µ ?
40
ATLAS’19
BR h →τµ( ) ≤ 0.28% 13 TeV@ATLAS ATLAS’19
• Constraints from Higgs decay (LHC) vs. low energy LFV and LFC observables
3.4 Constraints in the µe sector • Constraints: Higgs decays vs low-energy LFV and LFC observables
Plot from Harnik-Kopp-Zupan ’
1209.1397
* Diagonal couplings set to SM value
• μe sector: powerful low-energy constraints ⇒ BR(H→μe) < 10-7
• Best constraints coming from low energy: µ → eγ
Harnik, Kopp, Zupan’12
BR µ → eγ( ) < 5.7 10−13
MEG’13
BR h → µe( ) < 10−7
41 Emilie Passemar
4. Conclusion and Outlook
Summary
• Direct searches for new physics at the TeV-scale at LHC by ATLAS and CMS energy frontier
• Probing new physics orders of magnitude beyond that scale and helping to decipher possible TeV-scale new physics requires to work hard on the intensity and precision frontiers
• Charged leptons offer an important spectrum of possibilities:
Ø LFV measurements have SM-free signal
Ø Current experiments and mature proposals promise orders of magnitude sensitivity improvements
Ø In addition to leptonic and radiative decays hadronic decays important, e.g. τ → µ(e)ππ, µN → eN
Ø New physics models usually strongly correlate these sectors
Emilie Passemar 43
Summary
• Direct searches for new physics at the TeV-scale at LHC by ATLAS and CMS energy frontier
• Probing new physics orders of magnitude beyond that scale and helping to decipher possible TeV-scale new physics requires to work hard on the intensity and precision frontiers
• Charged leptons offer an important spectrum of possibilities:
Ø We show how CLFV decays offer an excellent model discriminating tools giving indications on - the mediator (operator structure) - the source of flavour breaking (comparison τ µ vs. τe vs. µe)
• Interplay low energy and collider physics: LFV of the Higgs boson
• Several experimental programs: MEG, Mu3e, COMET, Mu2e, Belle II, BESIII, LHCb, LHC-HL
Emilie Passemar 44